Question 2 (5 points)
(08.03 LC)
Factor completely: x2 + 7x + 10 (5 points)
a.(x + 5)(x + 2)
b.(x + 10)(x + 1)
c.(x2 + 5)(x + 2)
d .Prime

It's a

Step-by-step explanation:

This is a quadratic expression with the highest power of X being 2.

The coefficient of X² = 1

Note that the general form of a quadratic equation is aX² + bX + C

In this question,

a = 1

b = 7

C = 10

First step is to multiply a and C ( a x C)

= 1 X 10 = 10

Then, find 2 factors of 10 which can both add up to give 7, the coefficient of X given in the question.

The possible factors of 10 are 5 and 2. The sum of 5 and 2 is

5 + 2

Hence, the equation can be written as;

X² + 7X + 10 = X² + 5X + 2X + 10

The next step is to group using a bracket and factorise each bracket individually

(X² + 5X) + (2X + 10) =

X( X + 5) + 2( X + 5) =

(X + 5) (X + 2)

(X + 5) (X + 2) are the factors of the quadratic equation, X² + 7X + 10

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it